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Popular >

derivative of y=(3x-2)/x

Solution

derivative of

y = \frac{3 x - 2}{x}

Solution

\frac{2}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x - 2}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x - 2 ) x - \frac{d x}{d x} ( 3 x - 2 )}{x ^{2}}

\frac{d}{d x} (3 x - 2) = 3

\frac{d x}{d x} = 1

= \frac{3 x - 1 \cdot ( 3 x - 2 )}{x ^{2}}

Simplify

= \frac{2}{x ^{2}}

Popular Examples

derivative of (x^2-1/(x^3+x+1))

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3} + x + 1})

(\partial)/(\partial t)(4sin(t))

\frac{\partial}{\partial t} (4 sin (t))

area y= 1/2 x,y= 1/25 x^2,y=1 area

y = \frac{1}{2} x, y = \frac{1}{25} x^{2}, y = 1

limit as x approaches 5 of (2x)/(x-5)

x \to 5 lim (\frac{2 x}{x - 5})

limit as x approaches 9 of sqrt(f(x))

x \to 9 lim (f (x))

Frequently Asked Questions (FAQ)

What is the derivative of y=(3x-2)/x ?
The derivative of y=(3x-2)/x is 2/(x^2)
What is the first derivative of y=(3x-2)/x ?
The first derivative of y=(3x-2)/x is 2/(x^2)